We employ the method of reverse unitarity [1]} to express the phase-space integral over the squared decay amplitude for \(h\rightarrow \gamma \gamma gg\)  as
cut two-point forward-scattering diagrams. In each of these diagrams the Higgs bosons couple to different top-quark loops, which are connected to each other by the cut gluons and photons.
A sample diagram is shown in Fig. REF . A direct large-mass expansion of such five-loop diagrams is computationally expensive, thus we adopt the building-block approach
described in [2]}, [3]}; we pre-compute the 24 one-loop diagrams contributing to the \(h\gamma \gamma gg\)  vertex in the large-mass expansion. Since there are only hard
subgraphs, the result is polynomial in all external momenta and can be used as an effective vertex. As a consequence, instead of 120 five-loop diagrams, we only expand 24 one-loop diagrams which then are
inserted into the cut three-loop two-point diagram shown in Fig. REF . The resulting diagram can be computed using MINCER [4]}.
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